Discrete & Computational Geometry

, Volume 12, Issue 3, pp 367-384

First online:

Objects that cannot be taken apart with two hands

  • J. SnoeyinkAffiliated withDepartment of Computer Science, University of British Columbia
  • , J. StolfiAffiliated withComputer Science Department, Universidade Estadual de Campinas

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It has been conjectured that every configurationC of convex objects in 3-space with disjoint interiors can be taken apart by translation with two hands: that is, some proper subset ofC can be translated to infinity without disturbing its complement. We show that the conjecture holds for five or fewer objects and give a counterexample with six objects. We extend the counterexample to a configuration that cannot be taken apart with two hands using arbitrary isometries (rigid motions).